MatrixRank—Wolfram Language Documentation
reference.wolfram.com › language › refMatrixRank works on both numerical and symbolic matrices. The rank of a matrix is the number of linearly independent rows or columns. MatrixRank [ m, Modulus -> n] finds the rank for integer matrices modulo n. MatrixRank [ m, ZeroTest -> test] evaluates test [ m [ [ i, j]]] to determine whether matrix elements are zero.
Unitary Matrix -- from Wolfram MathWorld
https://mathworld.wolfram.com/UnitaryMatrix.html17.12.2021 · A square matrix U is a unitary matrix if U^(H)=U^(-1), (1) where U^(H) denotes the conjugate transpose and U^(-1) is the matrix inverse. For example, A=[2^(-1/2) 2^(-1/2) 0; -2^(-1/2)i 2^(-1/2)i 0; 0 0 i] (2) is a unitary matrix. Unitary matrices leave the length of a complex vector unchanged. For real matrices, unitary is the same as orthogonal. In fact, there are …
Matrix Rank -- from Wolfram MathWorld
mathworld.wolfram.com › MatrixRankDec 17, 2021 · Matrix Rank. The rank of a matrix or a linear transformation is the dimension of the image of the matrix or the linear transformation, corresponding to the number of linearly independent rows or columns of the matrix, or to the number of nonzero singular values of the map. The rank of a matrix is implemented as MatrixRank [ m ]. Weisstein, Eric ...